A flow built under a step function with a multistep Markov partition on a base
Abstract
It is proved that the flows built under step functions are dense in dmetric. Hence every flow can be approximated in distribution and entropy by flows, each being built under a step function with a multistep Markov partition on a base. It is proved that a flow under a step function with a multistep Markov partition on a base is a direct product of a Bernoulli flow with a rotation. Dclosure of this class is shown to consist of all direct products of Bernoulli flows with flows of rational pure point spectrum w.r.t. some number. Specially Bernoulli flows can be characterized as dlimits of Bernoulli flows in this class. It is demonstrated that a flow under a step function, whose values are independent over rationals, with a mixing Markov partition on a base is a Bernoulli type. But two nonisomorphic flows are also constructed (one is Bernoulli and the other is LB) under step functions, each having the property, that is values are independent over rationals, with the same Bernoulli partition on a base. It is also shown that every flow can be generated by three Bernoulli factors.
 Publication:

Ph.D. Thesis
 Pub Date:
 1980
 Bibcode:
 1980PhDT........52P
 Keywords:

 Flow Characteristics;
 Fluid Dynamics;
 Markov Processes;
 Partitions (Structures);
 Step Functions;
 Bernoulli Theorem;
 Entropy;
 Flow Distribution;
 Rotating Fluids;
 Fluid Mechanics and Heat Transfer